Methods for transport equations with random data / Metodos para equações do transporte com dados aleatorios

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

Mathematical models for real-world processes often take the form of systems of artial differential equations. Such models usually involve certain parameters, for example, the coefficients in the differential operator, and the initial and boundary conditions. Usually, all the model parameters are assumed to be known exactly. However, in realistic situations many of the parameters may have a random or stochastic character. More advanced models must take this stochastic nature into account. In this case, the components of the system are then modeled as random variables or random fields. Differential equations with random parameters are called random (or stochastic) differential equations. New mathematical methods have been developed to deal with this kind of problem, however, solving this problem is still the goal of several researchers. Thus, it is important to look for new approaches (numerical or analytical) to deal with random differential equations. Throughout the realization of the doctorate and looking toward future applications in porous media flow (pollution dispersal and two phase flows, for instance) we developed works related to the one-dimensional random linear transport equation and to the onedimensional random Burgers-Riemann problem. In this thesis, based on Godunov s ideas, we present a new methodology to deal with the one-dimensional random linear transport equation, and develop an efficient numerical scheme for the statistical moments of the solution of the one-dimensional random Burgers-Riemann problem. Finally, we also present new results for the multidimensional case: we have shown that some approaches to approximate the mean of the solution of the multidimensional random linear transport equation may be valid for all statistical moments of the solution.

ASSUNTO(S)

conservation laws (physics) leis de conservação (fisica) numerical methods stochastic differential equations metodos numericos equações diferenciais estocasticas

ACESSO AO ARTIGO

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